Using bootstrap resamples to generate a confidence interval
From your original sample, resample with replacement the same number of times as your original sample.
This is your bootstrap resample.
Repeat this process many, many times.
Calculate a numerical summary (e.g., mean, median) for each bootstrap resample.
These are your bootstrap statistics
Bootstrap Distribution
definition: a distribution of the bootstrap statistics from every bootstrap resample
Displays the variability in the statistic that could have happened with repeated sampling.
Approximates the true sampling distribution!
Penguins!
Statistic: \(\beta_1\)
The relationship between penguin’s bill length and body mass for all penguins in the Palmer Archipelago
Generating a bootstrap resample
Step 1: specify() your response and explanatory variables
specify()
Step 2: generate() bootstrap resamples
generate()
Step 3: calculate() the statistic of interest
calculate()
Declare your variables!
penguins %>% specify(response = bill_length_mm, explanatory = body_mass_g)
Generate your resamples!
penguins %>% specify(response = bill_length_mm, explanatory = body_mass_g) %>% generate(reps = 500, type = "bootstrap")
reps – the number of resamples you want to generate
reps
"bootstrap" – the method that should be used to generate the new samples
"bootstrap"
Calculate your statistics!
penguins %>% specify(response = bill_length_mm, explanatory = body_mass_g) %>% generate(reps = 500, type = "bootstrap") %>% calculate(stat = "slope")
"slope" – the statistic of interest
"slope"
stat
The final product
visualize(bootstrap) + labs(title = "Bootstrap Distribution of 500 reps", x = "Slope Statistic")
A plausible range of values for: \(\beta_1\)
The 95% confidence interval is…
get_confidence_interval(bootstrap, level = 0.95, type = "percentile")
